Results/Conclusions

Methods from the theory of slow-fast dynamical systems can be used to reduce model dimension back down to two (predator and prey abundance). This allows for some simple graphical analyses, based on tradeoff curves and transitions between periods of rapid evolutionary change and periods of evolutionary stasis, that let us catalog the different qualitative types of dynamics that can occur. Heritable variation in both predator and prey for traits affecting their interaction leads to coupled oscillator models where dynamics at the genotypic level may stabilize predator-prey cycles or lead to bursting-type behaviors at the population level. Methods from functional data analysis make it possible to infer properties of underlying trait dynamics from observations at the population level, raising the hope that observational data on food web dynamics could be used to draw conclusions about the role of unobserved trait dynamics.